Propagation of In-Plane Shear Waves in Magnetically Affected Highly Conductive Nanofilms by Considering Both Surface and Nonlocality Effects

Abstract

To study the size and surface effects on characteristics of in-plane shear waves in magnetically affected nanofilms, a novel model is developed. Using nonlocal and surface continuum theories, the governing equations are established and appropriate boundary conditions are imposed at the bottom and top surfaces of the nanofilm. The dispersion relations associated with symmetric and asymmetric modes are obtained. The effects of the surface energy, small-scale parameter, nanofilm's thickness, and magnetic field strength on dispersion curves are addressed. The limitations of the classical theory of elasticity are discussed. The obtained results show that the phase velocity of the propagated in-plane shear waves magnifies by an increase of the thickness as well as magnetic field strength. However, the phase velocity commonly decreases as the effect of the surface energy or nonlocality increases. Such a fact is more obvious for higher modes of vibration. Generally, the cutoff frequency reaches a lower value as the nanofilm's thickness reduces or the small-scale parameter increases. Additionally, variation of the magnetic field strength has fairly no influence on the cutoff frequency.